Besed　on　the　symmetry　properties　of　constrained　Hamiltonian　system,　we　present　one　other　example　to　show　that　Dirac’s　conjecture　fails　in　a　different　way　than　other　examples　in　that　there　is　no　linearization　of　constraint　in　this　problem.　A　clear　discussion　is　made　on　the　relationships　of　the　coefficients　connecting　with　the　first-class　constraints　in　the　gauge　generator　for　a　constrained　Hamiltonian　system.　The　results　of　this　counterexample　are　also　in　contradiction　with　the　other　conclusions.　©　1993　IOP　Publishing　Ltd.